Page 131 - Mechanics of Microelectromechanical Systems
P. 131
118 Chapter 2
and this enables formulating the integrals in terms of the compliances of the
second interval, 2-3 (where 2 is considered free and 3 fixed) as:
The superscript 2 in Eqs. (2.178) through (2.180) indicates the second (2-3)
symmetric segment of the microbridge of Fig. 2.36, and the compliances of
the same equations are calculated at point 2 (considered free) with respect to
the fixed point 3. Because the way in which the variables and have been
chosen, and because the two segments, 2-1 and 2-3, are identical, it follows
that any compliance denoted by the superscript 1 in Eqs. (2.175) through
(2.177) is identical to the corresponding compliance bearing the superscript 2
in Eqs. (2.178) through (2.180). As a consequence, Eqs. (2.172) permit
solving for the unknowns and in the form:
The superscript 2 indicates again that the compliances in Eqs. (2.181)
correspond to one symmetric half of the microbridge sketched in Fig. 2.36.
The deflection at midpoint 2 can now be found by using a procedure similar
to the one that gave the reactions at point 1, namely:
After performing the necessary calculations, it is found that the bending
stiffness is:
